Question

An archeologist claims to have unearthed some papyrus scrolls that pre-date the dead sea scrolls by at least 200 years – around 600 BCE. In your lab, working from a small sample of the scrolls, you find that the sample contains 0.80g of carbon, and you measure the rate of carbon-14 decay to be 10 decays per minute. Do you verify or refute the archeologist’s claim? [The fraction of all carbon atoms assumed to be carbon-14 when an organic tissue is still exchanging carbon with its environment is 1.3×10^(–12).]

Answer 1

0.8g of Carbon has atoms of carbon and hence initiallyatoms of radioactive carbon (C-14), when the tree was cut to make the papyrus scroll.

The half-life of C-14 is 5730 years. The equation for radiaoactive decay can be written as:

Differentiating this wrt time, we get the rate of decay as:

Solving this equation by substituting and the value of and half-life calculated above, we get:

or

years.

Thus the scroll is about 1500 years old, putting it at around 500 AD, and not as old as is claimed.